CUDA rendering on Linux Mint or Ubuntu variants
You will need to install the package nvidia-modprobe which (I believe) allows Blender to detect your nvidia CUDA device. This is applicable to Mint, Debian and Ubuntu, I don't know about other distributions of Linux:

sudo apt-get install nvidia-modprobe


You can also install nvidia-modprobe via your favourate package manager.
Please use the Nvidia drivers from the standard repo, the drivers from their website are not auto updated. Doing sudo blender for one feature is non-optimal :) and means that all your .blend files and exports will be owned by root. This is inconventient.

Note that Blender+Nvidia+CUDA requires nvidia-cuda-toolkit, nvidia-modprobe and the proprietary drivers.

Edit: Mint doesn't have a nvidia-modprobe package. 

Download the nvidia-modprobe coresponding to your nvidia driver from here then extract it.
Use a terminal to navigate (use cd [dir] to navigate) to the folder where you extracted the file. Run make and then run sudo make install to install nvidia-modprobe.

Alternatively use this to download and install the Ubuntu nvidia-modprobe package (not recomended):

wget -c "http://mirrors.kernel.org/ubuntu/pool/multiverse/n/nvidia-modprobe/nvidia-modprobe_340.24-1~ubuntu14.04.1_i386.deb" -o "nvidia-modprobe.deb"


And then:

sudo dpkg --force-install nvidia-modprobe.deb


You will need to reboot afterwards.
This should install the right package. You might want to submit a bug report to the Mint17 people for not including nvidia-modprobe.